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A136662 Number of cycles of the permutations of [1,2,...,n], for n=1,2,3,... 3
1, 2, 1, 3, 2, 2, 1, 1, 2, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 5, 4, 4, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 2, 4, 3, 3, 2, 2, 3, 3, 4, 2, 3, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 3, 2, 2, 1, 1, 2, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The row lengths sequence is A000142(n), n>=1, (factorials).

The permutations of [1,2,...,n] are ordered in the standard way (lexicographic or numerically increasing). E.g., in Maple as permute(n) list for not too large n (around 10).

LINKS

Alois P. Heinz, Rows n = 1..8, flattened

FindStat - Combinatorial Statistic Finder, The number of cycles in the cycle decomposition of a permutation

W. Lang, First rows and cycle decompositions.

FORMULA

a(n,k)= number of cycles of the k-th permutation of [1,2,...,n] in standard (increasing) order.

EXAMPLE

[1];[2,1];[3,2,2,1,1,2];[4,3,3,2,2,3,3,2,2,1,1,2,2,1,3,2,2,1,1,2,2,3,1,2];...

Row n=3: permutations of [1,2,3] in the order [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]. Cycle decomposition: [[[1], [2], [3]], [[1], [2, 3]], [[1, 2], [3]], [[1, 2, 3]], [[1, 3, 2]], [[1, 3], [2]]]. Number of cycles: [3,2,2,1,1], the entries of row n=3.

CROSSREFS

Row sums (total cycle numbers) A000254.

Cf. A130534.

Sequence in context: A035151 A290536 A277855 * A023595 A177718 A057515

Adjacent sequences:  A136659 A136660 A136661 * A136663 A136664 A136665

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Feb 22 2008, May 21 2008

STATUS

approved

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Last modified February 27 06:36 EST 2020. Contains 332299 sequences. (Running on oeis4.)